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Conference Papers Year : 2009

Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

Abstract

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.
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Dates and versions

hal-00163141 , version 1 (16-07-2007)
hal-00163141 , version 2 (31-08-2007)
hal-00163141 , version 3 (23-11-2007)
hal-00163141 , version 4 (27-01-2009)
hal-00163141 , version 5 (18-05-2009)

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Cite

Brice Boyer, Jean-Guillaume Dumas, Clément Pernet, Wei Zhou. Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm. ISSAC 2009 - International Symposium on Symbolic and Algebraic Computation, Jul 2009, Séoul, South Korea. pp.55-62, ⟨10.1145/1576702.1576713⟩. ⟨hal-00163141v5⟩
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